Pacific Journal of Mathematics

Interpolation between $H^p$ spaces and noncommutative generalizations. I.

Gilles Pisier

Article information

Pacific J. Math., Volume 155, Number 2 (1992), 341-368.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46M35: Abstract interpolation of topological vector spaces [See also 46B70]
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions 46L99: None of the above, but in this section 47Dxx: Groups and semigroups of linear operators, their generalizations and applications


Pisier, Gilles. Interpolation between $H^p$ spaces and noncommutative generalizations. I. Pacific J. Math. 155 (1992), no. 2, 341--368.

Export citation


  • [B] J. Bourgain, New Banach spaceproperties of the disc algebraand H , Acta Math., 152 (1984), 1-48.
  • [BB] R. P. Boas and S. Bochner, On a theorem of Marcel Rieszfor Fourierseries, J. London Math. Soc, 14 (1939), 62-73.
  • [BL] J. Bergh and J. Lfstrm, Interpolation Spaces, An Introduction, Springer- Verlag, 1976.
  • [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988.
  • [BuD] A. Bukhvalov and A. Danilevitch, Boundary properties of analytic and har- monic functions with values in a Banach space, Mat. Zametki, 31 (1982), 203-214; English translation: Math. Notes, 31 (1982), 104-110.
  • [BX] O. Blasco and Q. Xu, Interpolation between vector valued Hardy spaces, J. Funct. Anal., 102 (1991), 331-359.
  • [E] G. Edgar, Analytic martingale convergence, J. Funct. Anal., 69 (1986), 268- 280.
  • [G] J. Garnett,Bounded Analytic Functions, Academic Press, 1981.
  • [GK] I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfad- joint operators,Transl. Math. Monographs, Amer. Math. Soc, Providence, RI, 1969.
  • [GR] J. Garcia-Cuerva andJ. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics,North-Holland,1985.
  • [H] H. Helson, Lectures on Invariant Subspaces, Academic Press, NewYork, 1964.
  • [HP] U. Haagerup andG.Pisier, Factorisation of analytic functions with values in non-commutative L-spaces andapplications, Canad. J. Math., 41 (1989), 882-906.
  • [Jl] P.Jones, L estimates for the d-problem in a half plane, Acta Math.,150 (1983), 137-152.
  • [J2] P.Jones,Interpolation between Hardy spaces, in Conference onHarmonicAnal- ysis in honor of Antoni Zygmund, (edited by W. Beckner, A. Caldern, R. Fefferman and P.Jones), Wadsworth Inc., 1983,vol.2,pp. 437-451.
  • [JJ] S. Janson andP. Jones, Interpolation between Hp spaces: The complex method, J. Funct. Anal., 48 (1982), 58-80.
  • [KLW] V. Kaftal, D. Larson and G.Weiss, Quasitriangular subalgebras ofsemifinite von Neumann algebras areclosed,preprint, to appear. (Amer. J. Math.)
  • [K] S.V. Kisliakov, Truncatingfunctions in weighted Hp andtwo theorems of J. Bourgain, Preprint, Uppsala University,May 1989.
  • [KX] S. V. Kisliakov andQ. Xu, Sur Interpolation des espaces Hp , Comptes Rendus Acad. Sci. Paris 313 Serie I (1991), 249-255.
  • [M] P.Mller, Holomorphic martingales and interpolation of operators, J.Analyse Jerusalem. Toappear.
  • [P] G.Pisier,A simple proof of a theorem of Jean Bourgain, Michigan J. Math. To appear.
  • [PT] A. Pietsch and H. Triebel, Interpolationstheorie fur Banachideale von beschrnkten linearen operatoren, Studia Math., 31 (1968), 95-109.
  • [S] D. Sarason, Generalized interpolation in H ,Trans. Amer. Math. Soc, 127 (1967), 179-203.
  • [W] T.Wolff, A Note on Interpolation Spaces, SpringerLecture Notes in Math., 908 (1982), 199-204.
  • [XI] Q.Xu, Applications dutheoreme defactorisation pour desfonctons avaleurs operateurs, Studia Math., 95 (1989), 273-292.
  • [X2] Q.Xu, Real interpolation of some Banach lattices valued Hardy spaces, preprint, Pub.Irma, Lille (1990) vol.20, 8.
  • [X3] Q.Xu, Elementary proofs of two theorems of P. W. Jones on interpolation of Hardy spaces, preprint, Pub.Irma, Lille, (1989).

See also

  • Gilles Pisier. Interpolation between {$H\sp p$} spaces and noncommutative generalizations. {II}. II [MR 94g:46089] Rev. Mat. Iberoamericana 9 1993 2 281--291.